Question: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 4x + 1$ and $ KL = 8x - 27$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {4x + 1} = {8x - 27}$ Solve for $x$ $ -4x = -28$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 4({7}) + 1$ $ KL = 8({7}) - 27$ $ JK = 28 + 1$ $ KL = 56 - 27$ $ JK = 29$ $ KL = 29$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {29} + {29}$ $ JL = 58$